Critical Coupling Parameter Research Articles

In-phase and mixed-phase measure synchronization of camphor rotors.

The numerical, analytical, and experimental analyses are presented for synchronizing two rotors under the Yukawa interaction. We report that the rotors exhibit in-phase and mixed-phase measure synchronizations for a pair of coupled rotors. Here, the analytical condition for synchronization is derived, tested numerically, and confirmed experimentally using coupled camphor infused rotors as a test bed. Moreover, the concept of measure synchronization is discussed. We report that, in conservative systems, not only the critical coupling parameter but initial conditions also play an essential role for estimating the measure synchronization region.

Optimal time-varying coupling function can enhance synchronization in complex networks.

In this paper, we propose a time-varying coupling function that results in enhanced synchronization in complex networks of oscillators. The stability of synchronization can be analyzed by applying the master stability approach, which considers the largest Lyapunov exponent of the linearized variational equations as a function of the network eigenvalues as the master stability function. Here, it is assumed that the oscillators have diffusive single-variable coupling. All possible single-variable couplings are studied for each time interval, and the one with the smallest local Lyapunov exponent is selected. The obtained coupling function leads to a decrease in the critical coupling parameter, resulting in enhanced synchronization. Moreover, synchronization is achieved faster, and its robustness is increased. For illustration, the optimum coupling function is found for three networks of chaotic Rössler, Chen, and Chua systems, revealing enhanced synchronization.

One-Dimensional Confined Bose Gas in a Quartic Potential: Calculation of the Energy Levels and the Critical Coupling Parameter

Perturbation theory can be reformulated as dynamic theory applied to crystals and gases. Here we concentrate our attention on the stability conditions that allow controlling the convergence of approximation sequences. These ideas are illustrated by calculating the energy levels and critical coupling parameter of a one-dimensional confined Bose gas

Coupled dimer and bond-order-wave order in the quarter-filled one-dimensional Kondo lattice model

Motivated by the experiments on the organic compound $(Per)_{2}[Pt(mnt)_{2}]$, we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and bond-order-wave (BOW) state in the weak coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter $J_{c}$, with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such phase transition. We also show that the localized spins in this insulating state have quasi-long ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.

Hydrodynamic Quantum Field Theory: The Onset of Particle Motion and the Form of the Pilot Wave

We consider the hydrodynamic quantum field theory proposed by Dagan and Bush, a model of quantum dynamics inspired by Louis de Broglie and informed by the hydrodynamic pilot-wave system discovered by Couder and Fort. According to this theory, a quantum particle has an internal vibration at twice the Compton frequency that generates disturbances in an ambient scalar field, the result being self-propulsion of the particle through a resonant interaction with its pilot-wave field. Particular attention is given here to providing theoretical rationale for the geometric form of the wave field generated by steady, rectilinear particle motion at a prescribed speed, where signatures of both the de Broglie and Compton wavelengths are generally evident. While focus is given to the one-dimensional geometry considered by Dagan and Bush, we also deduce the form of the pilot wave in two dimensions. We further consider the influence on the pilot-wave form of the details of the particle-induced wave generation, specifically the spatial extent and vibration frequency of the particle. Finally, guided by analogous theoretical descriptions of the hydrodynamic system, we recast the particle dynamics in terms of an integro-differential trajectory equation. Analysis of this equation in the non-relativistic limit reveals a critical wave-particle coupling parameter, above which the particle self-propels. Our results provide the foundation for subsequent theoretical investigations of hydrodynamic quantum field theory, including the stability analysis of various dynamical states.

Scalarization of neutron stars with realistic equations of state

We consider the effect of scalarization on static and slowly rotating neutron stars for a wide variety of realistic equations of state, including pure nuclear matter, nuclear matter with hyperons, hybrid nuclear and quark matter, and pure quark matter. We analyze the onset of scalarization, presenting a universal relation for the critical coupling parameter versus compactness. We find that the onset and the magnitude of the scalarization are strongly correlated with the value of the gravitational potential (the metric component $g_{tt}$) at the center of the star. We also consider the moment-of-inertia--compactness relations and confirm universality for the nuclear matter, hyperon and hybrid equations of state.

Bond and flux-disorder effects on the superconductor-insulator transition of a honeycomb array of Josephson junctions

We study the effects of disorder on the zero-temperature quantum phase transition of a honeycomb array of Josephson junctions in a magnetic field with an average of fo flux quantum per plaquette. Bond disorder due to spatial variations in the Josephson couplings and magnetic flux disorder due to variations in the plaquette areas are considered. The model can describe the superconductor-insulator transition in ultra-thin films with a triangular pattern of nanoholes. Path integral Monte Carlo simulations of the equivalent (2 + 1)-dimensional classical model are used to study the critical behavior and estimate the universal resistivity at the transition. The results show that bond disorder leads to a rounding of the first-order phase transition for fo=1/3 to a continuous transition. For integer fo, the decrease of the critical coupling parameter with flux disorder is significantly different from that of the same model defined on a square lattice. The results are compared with recent experimental observations on nanohole thin films with geometrical disorder and external magnetic field.

Formation dynamics of jumps in systems of charged particles

The results of numerical studies of the dynamics of two similarly charged particles in an external electric field are presented. The formation of “jumps” (i.e., spontaneous changes in the positions) of the particles in a stable quasi-equilibrium state of the system has been analyzed in detail. Both dynamical and structural properties of the systems being modeled have been found to change significantly with rising particle temperature near some critical coupling parameter.

On multifractality and synchronization of nonlinear stellar pulsators

Simple models of nonlinear stellar pulsation, whose temporal behavior may reproduce some of the observed features of different classes of variable stars, have been studied. The temporal behavior of dynamical variables of these models exhibits a cascade of period doubling chaos, depending on the specific values of the various control parameters. A multifractal detrended fluctuation analysis (MFDFA) method is further used to identify the scaling behavior of such synthetic time series. The MFDFA of the considered time series, for various models of nonlinear stellar pulsation, shows that the observed multifractal nature is due to long-range correlations. The pulsating star with increased nonadiabaticity and the star with increased convective luminosity, as represented by the simulated data, is shown to possess a strange attractor with noninteger correlation dimension that lies between 2–3. Also the problem of synchronization in coupled nonlinear pulsation models has been investigated using permutation entropy—a complexity measure of the system. The computed order parameter, Γ, representing the correlation of computed permutation entropy for different segments of the simulated time series of displacement of two nonidentical oscillators, has been further used to find the critical coupling parameter for general synchronization of the oscillators.

Melting scenarios for three-dimensional dusty plasma clusters

The melting transition of finite three-dimensional dust clouds (Yukawa balls) from a solid-like to a liquid-like state is systematically studied with high spatial and temporal resolution of the individual grains by means of stereoscopy. Two different melting scenarios are reported: Melting is induced first by an increase of plasma power, and second by laser-induced heating. The experiments confirm that melting starts with a loss of orientational correlation, followed by a loss of the radial order upon further heating. While the plasma-power melting is driven via the ion wakefield, laser heating provides a more equilibrium scenario. The internal loss of correlations is well captured by the triple correlation function (TCF) which is insensitive to particle exchanges and the rotation of the cluster as a whole. The critical Coulomb coupling parameter for N=35 is determined as Γ(crit)≈570. The experimental findings are in good agreement with thermodynamic Monte Carlo simulations.

Anisotropic dark energy stars

A model of compact object coupled to inhomogeneous anisotropic dark energy is studied. It is assumed a variable dark energy that suffers a phase transition at a critical density. The anisotropic Lambda-Tolman-Oppenheimer-Volkoff equations are integrated to know the structure of these objects. The anisotropy is concentrated on a thin shell where the phase transition takes place, while the rest of the star remains isotropic. The family of solutions obtained depends on the coupling parameter between the dark energy and the fermion matter. The solutions share several features in common with the gravastar model. There is a critical coupling parameter that gives non-singular black hole solutions. The mass-radius relations are studied as well as the internal structure of the compact objects. The hydrodynamic stability of the models is analyzed using a standard test from the mass-radius relation. For each permissible value of the coupling parameter there is a maximum mass, so the existence of black holes is unavoidable within this model.

One-dimensional trapped atoms: critical coupling parameter and critical number of particles

In this paper we consider the case of a Bose gas in low dimension in order to illustrate the applicability of a method that allows us to construct analytical relations, valid for a broad range of coupling parameters, for a function which asymptotic expansions are known. The method is well suitable to investigate the problem of stability of a collection of Bose particles trapped in one- dimensional configuration for the case where the scattering length presents a negative value. The eigenvalues for this interacting quantum one-dimensional many particle system become negative when the interactions overcome the trapping energy and, in this case, the system becomes unstable. Here we calculate the critical coupling parameter and apply for the case of Lithium atoms obtaining the critical number of particles for the limit of stability.

Effects of a magnetic field on superconductivity and quantum criticality in quasi-two-dimensional systems with Dirac electrons

We study the effects of an external magnetic field on the superconducting phase diagram of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. At zero temperature, there is a quantum phase transition connecting a normal and a superconducting phase, occurring at a critical line that corresponds to a magnetic field dependent critical coupling parameter, which should be observed in planar materials containing Dirac electrons, such as Cu x TiSe 2 . Moreover, the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ( λ R ) . From this, we extract the critical magnetic field B c as a function of the temperature. For small values of B c , we obtain a linear decay of the critical field, which is similar to the behavior observed experimentally in the copper doped dichalcogenide Cu x TiSe 2 and also in intercalated graphite.

Magnetic field effects on the superconducting and quantum critical properties of layered systems with Dirac electrons

We study the effects of an external magnetic field on the superconducting properties of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. An explicit expression for the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ( λ R ) . From this, we extract the B × λ R , T × λ R and B × T phase diagrams. The last one shows a linear decay of the critical field for small values thereof, which is similar to the behavior observed experimentally in the copper doped dichalcogenide Cu x TiSe 2 and also in intercalated graphite. The second one, presents a coupling dependent critical temperature T c that resembles the one observed in high- T c cuprates in the underdoped region and also in Cu x TiSe 2. The first one, exhibits a quantum phase transition connecting a normal and a superconducting phase, occurring at a critical line that corresponds to a magnetic field dependent critical coupling parameter. This should be observed in planar materials containing Dirac electrons, such as Cu x TiSe 2.

Thermodynamic limit of the first-order phase transition in the Kuramoto model

In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter K(c). We obtain the asymptotic dependence of the order parameter above criticality: r-r(c)alpha(K - K(c))(2/3). For a finite population, we demonstrate that the population size N may be included into a self-consistency equation relating r and K in the synchronized state. We analyze the convergence to the thermodynamic limit of two alternative schemes to set the natural frequencies. Other frequency distributions different from the uniform one are also considered.

Laser heating of particles in dusty plasmas

Experiments on the heating and melting of two-dimensional finite dust crystals are performed using random laser excitation of the dust particles by a rapidly moving laser beam. The achievable dust temperatures scale with the square of the laser power. The heating process is described for different dust clusters under various plasma and cluster conditions. A single-particle model is developed to explain the observed behavior of the cluster under the random laser excitation. Good quantitative agreement is found when the radiation pressure is made responsible for the particle excitation by the laser. The dynamical properties of the system during heating are analyzed and the dominant modes are identified. From this, it is demonstrated that the heating process is of a nearly equilibrium nature in contrast to previous melting experiments. Finally, the melting of the dust cluster by laser heating is studied. From these experiments, a precise determination of the critical coupling parameter for the solid-fluid transition was possible. It is measured as Gamma = 270-480 for an N = 18 cluster.

Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators.

The transition to phase synchronization in systems consisting of a large number (N) of coupled nonlinear oscillators via the route of phase clustering (phase synchronization among subsets of oscillators) is investigated. We elucidate the mechanism for the merger of phase clusters and find an algebraic scaling between the critical coupling parameter required for phase synchronization and N. Our result implies that, in realistic situations, phase clustering may be more prevalent than full phase synchronization.

Scaling law for the fluid-solid phase transition in Yukawa systems (dusty plasmas)

Yukawa systems serve as models for plasmas and colloidal suspensions of charged particles. The state of these systems is determined by two dimensionless parameters: k = a/λD, which is the ratio of the mean interparticle distance to the Debye length λD, and Γ = Zd2e2/aTd, which is the ratio of the Coulomb potential energy to the particle temperature Td(Zd is the charge of each particle). We propose an empirical scaling law for the critical coupling parameter Γc needed for crystallization in Yukawa systems. The dependence of Γc on k is in good agreement with recent molecular dynamics simulations.

Phase transitions in lattices of coupled chaotic maps and their dependence on the local Lyapunov exponent

We study the continuous phase transitions in lattices of chaotic maps recently found by Miller and Huse. It is believed that in these lattices the order-disorder transition is generated by competition between (ordering) diffusion and (disordering) local chaos. As a test of this idea, we check whether the local Lyapunov exponent of the system behaves as a univocal extra control parameter for criticality. We verify the presence of phase transitions for a whole family of maps, both as function of coupling and of an internal parameter related to their chaoticity. We find that the critical coupling parameter is not a one-to-one function of the local Lyapunov exponent, which implies that this exponent cannot be used in general as control parameter for the transition.

Stability of bipolarons in the presence of a magnetic field

The stability of large Frohlich bipolarons in the presence of a static magnetic field is investigated with the path integral formalism. We find that the application of a magnetic field (characterized by the cyclotron frequence ω c) favors bipolaron formation: (i) the critical electronphonon coupling parameter α c (above which the bipolaron is stable) decreases with increasing ω c and (ii) the critical Coulomb repulsion strength U c (below which the bipolaron is stable) increases with increasing ω c. The binding energy and the corresponding variational parameters are calculated as a function of α, U and ω c. Analytical results are obtained in various limiting cases. In the limit of strong electron-phonon coupling (α ≫ 1) we obtain for ω c ≫ 1 that E estim ⋍ E estim(ω c = 0) + c(u)ω c/α 4 with c(u) an explicitly calculated constant, dependent on the ratio u = U/α where U is the strength of the Coulomb repulsion. This relation applies both in 2D and in 3D, but with a different expression for c(u). For ω c ≫ α 2≫ 1 we find in 3D E estim ⋍ ω c - α 2 A(u) ln2(ω c/α 2), (also with an explicit analytical expression for A(u)) whereas in 2D E estim 2D ⋍ ω c - α√ω cπ(u-2-√2)/2. The validity region of the Feynman-Jensen inequality for the present problem, bipolarons in a magnetic field, remains to be examined.